Abstract
We discuss some new approach for derivation of computational algorithms for certain types of evolution equations. The main idea of the algorithm is to make functional transformation of variables on the base of symmetry properties of pertinent physical system to make it quasi-diagonal. The approach is illustrated with the help of two important examples - the scattering in molecular system with elementary chemical reactions and the system of chemical kinetics for the many components system. The use of proposed approach show substantial speed-up over the standard algorithms and seems to be more effective with the increase of the size of the problem.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ebeling W., Freund J., Schweitzer F.: Komplexe Strukturen: Entropic und Information. B.G. Teubner, Stuttgart, Leipzig (1998)
Zakharov, V.E., Kuznetzov, E.A.: Hamiltonian formalism for nonlinear waves. In: Russian Uspekhi Fizicheskhich Nauk, Vol. 167. Nauka, Moscow (1997) 1137–1167
Itkin A.L., Kolesnichenko E.G.: Microscopic Theory of Condensation in Gases and Plasma. World Scientific, Singapore New Jersey London Hong Kong (1998)
Bogdanov A.V., Gorbachev Yu.E., Strelchenya V.M.: Relaxation and condensation processes influence on flow dynamics. in Proccedings of XV Intern. Symp. Rarefied Gas Dyn. Grado (Italy) (1986) 407–408
Topaler M., Makri N.: Multidimensional path integral calculations with quasidiabatic propagators: Quantum dynamics of vibrational relaxation in linear hydrocarbon chains. J.Chem.Phys. Vol. 97,12, (1992) 9001–9015
Greenberg W.R., Klein A., Zlatev I.: From Heisenberg matrix mechanics to semiclassical quantization: Theory and first applications. Phys. Rev. A Vol.54,3, (1996) 1820–1836.
Dubrovskiy G.V., Bogdanov A.V. Chem.Phys.Lett., Vol. 62,1 (1979) 89–94.
Bogdanov A.V.: Computation of the inelastic quantum scattering amplitude via the solution of classical dynamical problem. In:Russian Journal of Technical Physics, 7 (1986) 1409–1411.
A.V. Bogdanov, A.S. Gevorkyan, A.G. Grigoryan, Stankova E.N.: Use of the Internet for Distributed Computing of Quantum Evolution. in Proccedings of 8th Int. Conference on High Performance Computing and Networking Europe (HPCN Europe’ 2000), Amsterdam, The Netherlands (2000)
Bogdanov A.V., Dubrovskiy G.V., Gorbachev Yu.E., Strelchenya V.M.: Theory of vibration and rotational excitation of polyatomic molecules. Physics Reposrts, Vol.181,3, (1989) 123–206.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bogdanov, A.V., Stankova, E.N. (2001). The Use of Intrinsic Properties of Physical System for Derivation of High-Performance Computational Algorithms. In: Hertzberger, B., Hoekstra, A., Williams, R. (eds) High-Performance Computing and Networking. HPCN-Europe 2001. Lecture Notes in Computer Science, vol 2110. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48228-8_21
Download citation
DOI: https://doi.org/10.1007/3-540-48228-8_21
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42293-8
Online ISBN: 978-3-540-48228-4
eBook Packages: Springer Book Archive